Origami Heaven

A paperfolding paradise

The website of writer and paperfolding designer David Mitchell

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Nolids and Planar Designs
 
Nolids are solids of no volume. They can be viewed as composed of triangular sections of planes which run from the centre of symmetry of a polyhedron to its edges. In modular origami nolids paper modules replace and represent these imaginary planes.

Three of these nolids are special cases in which the triangular planes line up to form larger sections of planes that are polygonal in shape. Viewed in this way, the nolid or planar octahedron is composed of three interpenetrating squares, the nolid or planar cuboctahedron of four interpenetrating hexagons and the nolid or planar icosidodecahedron of six interpenetrating decagons.

Similarly my Four Octahedra can be seen as being composed of six interpenetrating 2x1 rectangles and my 12 Interpenetrating Pentagonal Rings as being composed of, well, the title says it all really!
 
 
 
  Name: Nolid or Planar Octahedron (2-part)

Modules / Paper shape / Folding geometry: 2 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1988.

Reference: 542

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
  Name: Nolid or Planar Octahedron (12-part) - three interpenetrating squares - not the same modular method as Robert Neale's similar looking design.

Modules / Paper shape / Folding geometry: 12 modules from silver rectangles.

Designer / Date: David Mitchell, 2002

Reference: 247

Diagrams: Diagrams not yet available.
 
  Name: Nolid or Planar Tetrahedron

Modules / Paper shape / Folding geometry: 6 modules from silver rectangles.

Designer / Date: David Mitchell, 1988 / Ian Harrison.

Reference: 366

Diagrams: In Mathematical Origami - David Mitchell - Tarquin publications - ISBN 9781911093169
 
  Name: Nolid or Planar Cube - robust design developed from David Brill's more delicate original.

Modules / Paper shape / Folding geometry: 12 modules from silver rectangles using silver rectangle folding geometry.

Designer / Date: David Mitchell, 2012.

Reference:342

Diagrams: Diagrams not yet available.
 
  Name: Nolid or Planar Cube with Nolid or Planar Tetrahedra

Modules / Paper shape / Folding geometry: Made by adding 30 modules, of two kinds, all folded from silver rectangles, to David Brill's Nolid Cube.

Designer / Date: David Mitchell, 2002. Based on a previous design by Ian Harrison.

Reference:

Diagrams: In Mathematical Origami - David Mitchell - Tarquin publications - ISBN 9781911093169
 
  Name: Six Interpenetrating Planes in a Cube

Modules / Paper shape / Folding geometry: Made by adding 30 modules, of two kinds, all folded from silver rectangles, to David Brill's Nolid Cube.

Designer / Date: David Mitchell, 2002.

Reference: 246

Diagrams: In Mathematical Origami - David Mitchell - Tarquin publications - ISBN 9781911093169
 
  Name: Nolid or Planar Cuboctahedron - four interpenetrating hexagons.

Modules / Paper shape / Folding geometry: 24 modules from hexagons, squares or double bronze rectangles using 60/30 degree geometry.

Designer / Date: David Mitchell, 1988.

Reference: 028

Diagrams: Mathematical Origami - Tarquin Publications - ISBN 1-899618-18-X (from double bronze rectangles) // In Portuguese - Origami matematicos - Republicao - ISBN 972-570-257-3 // Mathematical Origami - David Mitchell - Tarquin publications - ISBN 9781911093169
 
  Name: Nolid or Planar Dodecahedron

Modules / Paper shape / Folding geometry: 30 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1988.

Reference: 029

Diagrams: Not yet available.
 
  Name: Nolid or Planar Icosidodecahedron - six interpenetrating decagons. Not robust.

Modules / Paper shape / Folding geometry: 60 modules folded from squares using mock platinum folding geometry.

Designer / Date: David Mitchell, 1990.

Reference: 065

Diagrams: In Mathematical Origami - David Mitchell - Tarquin publications - ISBN 9781911093169
 
  Name: Four Octahedra - four Robert Neale Octahedra linked with joining pieces from squares. Larger versions are possible. .

Modules / Paper shape / Folding geometry: Each Robert Neale Octahedron is made from 6 modules from squares using standard folding geometry. Each joining piece is from a square using standard folding geometry.

Designer / Date: David Mitchell, 2016. Update of work from 1995.

Reference:

Diagrams: Not yet available.
 
  Name: 12 Interpetrating Pentagonal Rings

Modules / Paper shape / Folding geometry: Developed from the 60-part Corner-pocket Sonobe Spiky Star by the addition of 30 extra modules to link the vertexes together into rings. All modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1995.

Reference:

Diagrams: Not yet available.